Torment is the highest difficulty setting in Diablo III, replacing the earlier Inferno difficulty. It is unlocked when one character on the account reaches level 60, regardless of whether or not Reaper of Souls is installed. It is broken into 10 different levels, adjustable at will.
Torment VII-X can now only be accessed by level 70 characters
Torment VII-X public games can now only be accessed by players that meet a Paragon level requirement:
Torment VII requires a Paragon level over 100
Torment VIII requires a Paragon level over 150
Torment IX requires a Paragon level over 200
Torment X requires a Paragon level over 250